On Fibonacci functions with Fibonacci numbers

被引：9
|
作者：
Han, Jeong Soon [1 ]
Kim, Hee Sik [2 ]
Neggers, Joseph [3 ]
机构：
[1] Hanyang Univ, Dept Appl Math, Ahnsan 426791, South Korea
[2] Hanyang Univ, Dept Math, Res Inst Nat Sci, Seoul 133791, South Korea
[3] Univ Alabama, Dept Math, Tuscaloosa, AL 35487 USA
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2012年
关键词：
Fibonacci function; f-even (f-odd) function; Golden ratio;
D O I：
10.1186/1687-1847-2012-126
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider Fibonacci functions on the real numbers R, i.e., functions f : R -> R such that for all x is an element of R, f(x + 2) = f(x + 1) + f(x). We develop the notion of Fibonacci functions using the concept of f f-even and f-odd functions. Moreover, we show that if f is a Fibonacci function then lim(x ->infinity) f(x+1)/f(x) = 1+root 5/2.
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页数：7
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